184 



EEPORT — 1882. 



points. It is proved by von Oettingen that the correction for an initial 

 point i,. is given by 



f (i,.) := H^ — i,. + constant 

 = h,. + constant. 



Now, if the assumption is made that the correction for the highest 

 initial point is accurately given by the first mean curve, the corrections 

 for the initial points are readily found by adding to the values of h^ in 

 Table XIX., or /;,. — m in Table XXIII., the quantity which is necessary 

 to make /^lo or /i,o — m equal to the correction thus obtained from the 

 curve. 



Thus, in the example under discussion, the ordinate of the first mean 

 curve at 116° is — -024. To make the value of ^,o — m — viz. -079 — 

 equal to this, -103 must be subtracted from it. Hence the correction for 

 98° is — -191 — -103 = - -294, and so on. The quantities so obtained 

 are plotted down in fig. 1, Plate II., and produce the first initial point 

 curve (PQ R). 



In order to combine this with the portions of the upper point cor- 

 rection curves which extend below 116°, von Oettingen gives to it equal 

 weight with them, takes the mean, and thus completes the first approxi- 

 mation correction-curve. 



The corrections for the initial points thus determined are inserted in 

 Table XXV. :— 



Table XXV. 



Table XXVI. 



Corrections of Upper Ends from, mean curve I. (Jiff. 2., Plate II.) exjjressed 



'in terms of 0°-001. 



